Bisect / Cut Along Vertices That Are Selected?
There is a Bisect Operator that might do what you want it to.

3D View > Mesh > Bisect, requires a Face Selection

This allows you to split the mesh along a plane you can define by dragging, or numerically. If your Operator Panel is not open, hit F6 to show it. It come with a bunch of useful options, like

Fill, which fills the cut edges with faces
Clear Inner/Outer which remove one or both sides of the cut
Axis Threshold that gives the cut adge some fuzzines in where the cut-off happens.

If your vertices are already defining you cutting edge, it would be more efficient to simply separate the part into its own mesh by selecting it and hitting P to do Separate > Selection